Heat-Diffusion-1D

This is a software providing a solution to the heat diffusion in a 1D structure.

We consider:

Piecewise homogeneous materials
Electron system heating with a Gaussian like source
Two temperature model: electron & lattice temperature

The equation under consideration is:

where C = specific heat, k = conductivity, G is the coupling constant between the two systems (Electron and Lattice) and are the respective temperatures of the electron and the lattice system with respect to space x and time t. The super letters L and E indicate wether a parameter belongs to the electron or lattice system and the sub index i denotes to which layer the parameter belongs.

Our approach is to use a combination of finite elements (B-Splines) to approximate the derivation in space and Explicit Euler to approximate the evolution in time. To stay within the stability region of the Explicit Euler algorithm, a well suited time step is automatically computed.

Example:

In this case the Material under consideration is one layer of Strontium Ruthenium Oxide and one layer of Strontium Titanium Oxide behind it.

The output of the solver is the temperature evolution of the electron and lattice system in space and time.

Temperature evolution of electron- lattice system	Gaussian laser pulse S(x,t) hitting sample

Here we consider a laser source S(x,t) = lambda * exp(-lambda * (x-x0)) * G(t-t0) hitting a material from the left. I.e. Gaussian shape in time and exponentially decaying in space, according to Lambert-Beer’s law.

We can see the following effects in the animation:

The electron system immediately gets heated up.
Diffusion of the electron heating along the x-axis
Heat gets transported to the lattice system

Documentation

Documentation and example sessions can be found in the Wiki

With:

This is a project from the Ultrafast Condensed Matter physics groupe in Stockholm. The main contributors are:

Dependencies:

Numpy

Matplotlib

B-splines

How to contribute :